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\begin{document}

\title{Foray into the topology of poly-bi-{[}8{]}-annulenylene}



\author[1]{Varadharajan Muruganandam}%
\author[1]{Manas Sajjan}%
\author[1]{Sabre Kais}%
\affil[1]{Purdue University}%


\vspace{-1em}



  
  \date{May 25, 2024}


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\begin{abstract}
Analyzing phase transitions using the inherent geometrical attributes of
a system has garnered enormous interest over the past few decades. The
usual candidate often used for investigation is graphene- the most
celebrated material among the family of tri co-ordinated graphed
lattices. We show in this report that other inhabitants of the family
demonstrate equally admirable structural and functional properties that
at its core are controlled by their topology. Two interesting members of
the family are Cylooctatrene(COT) and COT-based polymer:
poly-bi-{[}8{]}-annulenylene both in one and two dimensions that have
been investigated by polymer chemists over a period of 50 years for its
possible application in batteries exploiting its conducting properties.
A single COT unit is demonstrated herein to exhibit topological solitons
at sites of a broken bond similar to an open one-dimensional
Su-Schrieffer-Heeger (SSH) chain. We observe that
Poly-bi-{[}8{]}-annulenylene in 1D mimics two coupled SSH chains in the
weak coupling limit thereby showing the presence of topological edge
modes. In the strong coupling limit, we investigate the different
parameter values of our system for which we observe zero energy modes.
Further, the application of an external magnetic field and its effects
on the band-flattening of the energy bands has also been studied. In 2D,
poly-bi-{[}8{]}-annulenylene forms a square-octagon lattice which upon
breaking time-reversal symmetry goes into a topological phase forming
noise-resilient edge modes. We hope our analysis would pave the way for
synthesizing such topological materials and exploiting their properties
for promising applications in optoelectronics, photovoltaics, and
renewable energy sources.%
\end{abstract}%



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